New A4 lepton flavor model from S4 modular symmetry

Liu

et al. 2019

129

In the modular symmetry approach to neutrino models, the flavour symmetry emerges as a finite subgroup Γ N of the modular symmetry, broken by the vacuum expectation value (VEV) of a modulus field τ . If the VEV of the modulus τ takes some special value, a residual subgroup of Γ N would be preserved. We derive the fixed points τ S = i, τ ST = (−1 + i √ 3)/2, τ T S = (1 + i √ 3)/2, τ T = i∞ in the fundamental domain which are invariant under the modular transformations indicated. We then generalise these fixed points to τ f = γτ S , γτ ST , γτ T S and γτ T in the upper half complex plane, and show that it is sufficient to consider γ ∈ Γ N . Focussing on level N = 4, corresponding to the flavour group S 4 , we consider all the resulting triplet modular forms at these fixed points up to weight 6. We then apply the results to lepton mixing, with different residual subgroups in the charged lepton sector and each of the right-handed neutrinos sectors. In the minimal case of two right-handed neutrinos, we find three phenomenologically viable cases in which the light neutrino mass matrix only depends on three free parameters, and the lepton mixing takes the trimaximal TM1 pattern for two examples. One of these cases corresponds to a new Littlest Modular Seesaw based on CSD(n) with n = 1 + √ 6 ≈ 3.45, intermediate between CSD (3) and CSD(4). Finally, we generalize the results to examples with three right-handed neutrinos, also considering the level N = 3 case, corresponding to A 4 flavour symmetry. *

Section: Introductionmentioning

confidence: 99%

Modular S4 and A4 symmetries and their fixed points: new predictive examples of lepton mixing

Liu

et al. 2019

129

“…This has led to a revival of the idea that modular symmetries are symmetries of the extra dimensional spacetime with Yukawa couplings determined by their modular weights [25,26]. The finite modular subgroups considered in the literature include Γ(2) [27][28][29][30], Γ(3) [25][26][27][28][31][32][33][34], Γ(4) [35][36][37] and Γ (5) [38,39]. The Γ(3) case has been applied to grand unified theories with the modulus fixed by the orbifold construction [40].…”

Section: Introductionmentioning

confidence: 99%

Modular A4 symmetry models of neutrinos and charged leptons

Liu

2019

124

We present a comprehensive analysis of neutrino mass and lepton mixing in theories with A 4 modular symmetry, where the only flavon field is the single modulus field τ , and all masses and Yukawa couplings are modular forms. Similar to previous analyses, we discuss all the simplest neutrino sectors arising from both the Weinberg operator and the type I seesaw mechanism, with lepton doublets and right-handed neutrinos assumed to be triplets of A 4 . Unlike previous analyses, we allow right-handed charged leptons to transform as all combinations of 1, 1 and 1 representations of A 4 , using the simplest different modular weights to break the degeneracy, leading to ten different charged lepton Yukawa matrices, instead of the usual one. This implies ten different Weinberg models and thirty different type I seesaw models, which we analyse in detail. We find that fourteen models for both NO and IO neutrino mass ordering can accommodate the data, as compared to one in previous analyses, providing many new possibilities. *

“…The finite modular groups Γ 2 ∼ = S 3 [3][4][5][6], Γ 3 ∼ = A 4 [1,3,4,[7][8][9][10][11][12][13][14], Γ 4 ∼ = S 4 [13,[15][16][17][18][19]] and Γ 5 ∼ = A 5 [18,20,21] have been considered. For example, simple A 4 modular models can reproduce the measured neutrino masses and mixing angles [1,8,12].…”

Section: Jhep08(2020)164mentioning

confidence: 99%

Modular invariant models of leptons at level 7

et al. 2020

We consider for the first time level 7 modular invariant flavour models where the lepton mixing originates from the breaking of modular symmetry and couplings responsible for lepton masses are modular forms. The latter are decomposed into irreducible multiplets of the finite modular group Γ 7 , which is isomorphic to PSL(2, Z 7), the projective special linear group of two dimensional matrices over the finite Galois field of seven elements, containing 168 elements, sometimes written as PSL 2 (7) or Σ(168). At weight 2, there are 26 linearly independent modular forms, organised into a triplet, a septet and two octets of Γ 7. A full list of modular forms up to weight 8 are provided. Assuming the absence of flavons, the simplest modular-invariant models based on Γ 7 are constructed, in which neutrinos gain masses via either the Weinberg operator or the type-I seesaw mechanism, and their predictions compared to experiment.